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We measure the branching fractions and CP asymmetries in the decays B0-->K(+)K(-)K(0)(S) and B+-->K(+)K(0)(S)K(0)(S) using a sample of approximately 122x10(6) BB pairs collected by the BABAR detector. From a time-dependent analysis of the K(+)K(-)K(0)(S) sample that excludes phiK(0)(S), the values of the CP-violation parameters are S=-0.56+/-0.25+/-0.04 and C=-0.10+/-0.19+/-0.10, where the …